Expression of type Conditional

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, k, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(ScalarMult(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Mult(two, pi, i, _phase, two_pow_t))), TensorProd(ket1, NumKet(k, t))), InSet(k, Interval(zero, subtract(two_pow_t, one))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	37, 9
7	Operation	operator: 33 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Operation	operator: 43 operands: 21
16	Operation	operator: 43 operands: 22
17	Operation	operator: 23 operand: 42
18	Operation	operator: 24 operands: 25
19	Literal
20	Operation	operator: 26 operands: 27
21	ExprTuple	29, 28
22	ExprTuple	29, 30
23	Literal
24	Literal
25	ExprTuple	37, 46
26	Literal
27	ExprTuple	41, 31
28	Operation	operator: 33 operands: 32
29	Literal
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operand: 42
32	ExprTuple	45, 38, 39, 40, 37
33	Literal
34	ExprTuple	45, 38, 39, 40, 41
35	Literal
36	ExprTuple	42
37	Variable
38	Literal
39	Literal
40	Literal
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Variable